Periodic error in heterodyne displacement-measuring interferometry is well known in the art. Researchers have identified and modeled sources of non-linearity in traditional Michelson-type heterodyne interferometers. Additionally, experimental configurations are known which tend to minimize or eliminate the periodic error inherent in these systems. Although such techniques have been successfully implemented, they typically require complex mechanical and/or electrical manipulations and are generally absent from commercial applications.
A fundamental source of systematic error in Michelson-type heterodyne interferometers is undesired leakage of each of the two polarization-coded light frequencies into both measurement and reference paths. In a perfect system, a single wavelength would travel to a fixed reference target, while a second, single wavelength should travel to a moving target. Interference of the combined signals would yield a perfectly sinusoidal trace with a phase that varied relative to a reference phase signal, in response to the motion of the moving target. The inherent frequency leakage of the two signals in actual implementations, however, tends to produce interference, or beat, signals, which are not exactly sinusoidal (i.e. contains spurious spectral content) and can lead to a periodic, or non-cumulative, error in measured displacements.
Experimental and analytical analyses of measurement signal frequency content have identified both first and second-harmonic periodic errors, or errors of one and two cycles per wavelength of optical path change, respectively. Physically, these errors arise from frequency leakage in the laser light source (non-orthogonality between the two frequencies exiting the laser head and ellipticity of the ideally linear output polarizations), non-ideal optical components (imperfect extinction between the two polarizations in the polarizing beamsplitter and retroreflector polarization rotation), mechanical misalignment of the interferometer (e.g. roll of the laser coordinate system with respect to the interferometer), parasitic reflections, and two-tone intermodulation distortions in the amplifying electronics.
FIG. 1 depicts a schematic diagram of a prior art heterodyne interferometer system 100. The setup for a typical, commercially available single pass heterodyne interferometer is also depicted in FIG. 1. As indicated in FIG. 1, system 100 generally includes a polarizing beamsplitter 106 in association with a measurement retroreflector 108 and a reference retroreflector 102. A light beam 110 can be transmitted from a laser light source (not shown in FIG. 1). Light beam 110 then encounters polarizing beamsplitter 106, such that a split portion of the light from light beam 110 is forced at a 90-degree angle to the original light beam 110 toward reference retroreflector 102. The portion of light beam 110 directed toward reference retroreflector 102 is ideally composed of light of frequency f1, but includes light of frequency 104 (i.e., f2) due to frequency leakage from one or more sources. Another portion of light beam 110, composed ideally of light with frequency f2, can continue in a straight path toward measurement retroreflector 108. A returning light beam 112 possesses a Doppler-shifted frequency of f2+(f1)±Δfd and also encounters polarizing beamsplitter 106 and passes on to a light detector (not shown in FIG. 1).
Because of the effect of leakage, each optical frequency may be present in both the reference and measurement paths of the interferometer. Detection of the interference signal during constant-velocity motion of the measurement retroreflector 108 exhibits multiple spectral peaks if this leakage exists. FIG. 2, for example, illustrates a graph 200 depicting a representation of the heterodyne interferometer frequency spectrum for low velocity target motion. The desired AC interference measurement signal 206 is seen at a frequency equal to the beat frequency (i.e. the difference between the two optical source frequencies, fb) up or down-shifted, depending on target direction, by a scalar amount proportional to the velocity of the moving retroreflector (i.e. the Doppler shift, Δfd).
With a proper alignment of the measurement beam and axis motion, the measurement signal amplitude can effectively remain constant during motion of the moving retroreflector. Also present, however, is spectral content that essentially remains at the beat frequency, known as spatial first-harmonic or AC reference terms 208, and a peak up or down-shifted from the beat frequency by an amount equal to, but opposite the measurement signal frequency shift, referred to as the second-harmonic or leakage-induced AC interference term 210.
Optical power terms 202 may also be observed at zero frequency and DC interference terms 204 at +Δfd in fully leaking configurations, when each source frequency exists in both the measurement and reference paths. For low target velocities and the typical phase locked loop (PLL) modulation bandwidths associated with phase measuring electronics in commercially available systems, however, it is the AC reference and leakage-induced AC interference terms that generally dominate the periodic error magnitude. The attenuation of these error signals with respect to the measurement signal determines the peak-to-peak value of the resulting periodic error. Reported values have ranged from approximately 0.4 nm to 12 nm.
Based on the foregoing, the present inventors have concluded that a need exists for an improved interferometer, which is not plagued by the problems associated with prior art interferometer systems. In particular, the present inventors believe that a need exists for an improved displacement measuring interferometer (DMI), which does not rely on polarization coding and polarization-dependent optics to separate and recombine the reference and measurement frequencies of the heterodyne system. Therefore, a new concept for a heterodyne interferometer that minimizes periodic error, while maintaining a simple architecture, is described and illustrated herein.